There are a number of potential "standard" treatments for cancer involving the liver and/or bile ducts. One possible approach, surgical removal, is frequently not to be possible. Another therapy is drug treatment (chemotherapy). However, currently available intravenous (given by vein) drug treatment has had limited value (only about 20% of patients show tumor shrinkage). A third approach is radiation therapy alone. As with chemotherapy alone, radiation therapy alone given once a day has had limited success. We are attempting to develop a more effective therapy for the treatment of these cancers. We are investigating the effectiveness and side effects of chemoembolization with a standard anticancer medication called mitomycin C. Chemoembolization involves injecting mitomycin C into an artery which supplies some of the blood to the liver (the hepatic artery), and immediately afterward, injecting small particles to stop some of the blood flow. Before the chemoembolization is given, a two week course of two other standard chemotherapy drugs (fluorodeoxyuridine and leucovorin) will be given by the hepatic artery at the same time that radiation is given to the liver. These other drugs can produce antitumor effects by themselves and can improve the effectiveness of the radiation. There is a considerable amount of experience with chemoembolization. Such treatment after liver radiation with hepatic arterial fluorodeoxyuridine and leucovorin has not been tested. Because we are trying to determine how much mitomycin C can be given, some patients will receive more of the medication than other people. The number of patients to be treated on this research protocol will be approximately 60-70 over a 5 year period of time. The outcomes we will study include toxicity (i.e., the severity of side effects), change in tumor size, and survival.